Math 454, Fall 2007

The course will emphasize the art of counting. It begins with chapter 2 and then jumps to part II. The aim is to cover chapters 5, 6, and 7. (Chapter 8 would be a nice conclusion to this theme, but it requires some acquaintance with abstract algebra.) Some fragments of chapter 3 may be introduced as needed. If we complete this, we will move into chapter 9. Here is the syllabus that evolved on the Sakai site.

- 09/05: Sections 2.1 and 2.2:
- 2.1: 2, 8.
- 2.2: 1, 2, 7.

- 09/10: Sections 2.3, 2.4 and 2.5:
- 2.3: 3, 6, 8.
- 2.4: none.
- 2.5: 3.

- 09/12: Sections 2.6 and 2.7:
- 2.6: 5, 6.
- 2.7: 8.

- 09/17: Sections 2.8 and 2.9:
- 2.8: 2, 10, 14.
- 2.9: 5, 8.

- 09/19: Sections 2.10 and 2.11:
- 2.10: 8, 10, 13.
- 2.11: 2.

- 09/24: Sections 2.12, 2.13 and 2.14:
- 2.12: 3, 4.
- 2.13: 2, 6.
- 2.14: 2, 7.

- 09/26: Sections 2.15, 2.16 and 2.17:
- 2.15: 2, 4.
- 2.16: 2, 4, 5.
- 2.17: 2.

- 10/01: Sections 2.18 and 2.19:
- 2.18: 9 (a, c, f, i, n only).
- 2.19: 8, 9, 18.

- 10/03: Chapter 2 summary
- No homework, but the availability of Additional Exercises on page 111 was mentioned./

- 10/08: Additional review of Chapter 2 and start chapter 4
- 4.1: 1,19,20.
- 4.2: 1, 13.

- 10/10: Exam on Chapter 2.
- 10/15: Sections 4.3 and 4.4
- 4.3: 4, 19, 20.(This was not intended. Theoretical considerations are not emphasized in this course. I intended to assign 4 and 8, but a previous entry was copied without being cleared for the new assignment. Problem 4 is hard enough, and part of problem 8 should be done as part of a complete solution to problem 4.)
- 4.4: 2, 12.

- 10/17: Further discussion of chapter 4. Homework deadline extended to 10/24.
- 10/22: Sections 5.1 and 5.2
- 5.1: 5, 13.
- 5.2: 5, 6, 10.

- 10/24: Sections 5.3
- 5.3: 2, 5, 7.

- 10/29: Sections 5.4
- 5.4: 2, 9, 15.

- 10/31: Sections 5.5
- 5.5: 4, 5.

- 11/05: Sections 5.6
- 5.6: 6, 7.

- 11/07: Sections 5.7
- 5.7: 1, 4.

- 11/12:
Sections 6.3 (This includes examples started in section 6.1; section
6.2 will be done later. These problems are due on Monday, 11/26)
- 6.3: 2, 4 (b and f only), 27.
- Verification of solution to differential equation from second supplement on twice-visited cities problem.

- 11/14: Review
- 11/19: Exam on chapter 4 and first 5 sections of chapter 5.
- Although chapter 6 is not explicitly included, recurrences are frequently used to identify generating functions, so some of the topics from section 6.3 may aid your knowledge of chapter 5.
- Note that this is the only scheduled meeting of this course this week.

- 11/26: Discussion of exam, and material from a supplement on generating functions.
- One exercise in supplement.

- 11/28: Sections 6.2 and 7.1
- 6.2: 5(a-e only), 9.
- 7.1: 7, 8, 11, 21.

- 12/3, 12/5, 12/10, 12/12: Review and highlights of Chapter 9.
- No new homework is assigned to allow time for previous work to be submitted, evaluated and returned. Topics without homework will not apear on the exam, but sections 5.7, 6.2, 6.3, 7.1 covered since the second midterm are possible topics for the final exam.